X Ray Physics - DSpace@MIT Home
X Ray PhysicsMIT Department of Physics(Dated: February 8, 2005)This lab investigates the production and absorption of X rays. You will verify Moseley’s lawand make measurements of the fine structure of the K lines of various elements. A cooled intrinsicgermanium solid state X ray detector is used to measure the spectra of X rays under a variety ofcircumstances that illustrate several of the important phenomena of X ray physics. Phenomenaobserved and measured include the production of X rays by fluorescent excitation, bremsstrahlung,and electron positron annihilation and the absorption of X rays by photoelectric interactions, Comp ton scattering, and pair production. The energies of the K X ray lines of numerous elements aremeasured and compared with the predictions of Moseley’s Law. The energy separations and relativeintensities of the Kα and Kβ lines are measured and compared with the theory of fine structure inthe n 2 orbitals.1.PREPARATORY QUESTIONS1. What are the possible ways in which photons withenergies in the range from 1 to 2000 keV can inter act with matter? (see Reference [1] or similar).2. How does a germanium solid state detector work?(see Reference [2] or similar).3. What atomic transitions give rise to the X ray lineslabeled K L3 (Kα1 ), K L2 (Kα2 ) and K M3(Kβ1 ) (see References [3, 4] or similar).4. According to the CRC Handbook [5], the total crosssection of lead for interaction with 24.94 keV X raysis 48.2 cm2 g 1 i.e. the total interaction cross sec tion of all the atoms in 1 gram of lead is 48.2 cm2 ).By what factor would the intensity of a pencil beamof such X rays be reduced by passage through 0.01cm of lead?5. Plot a curve of the expected energy E of Kα X raysagainst the atomic number Z .2.INTRODUCTIONIn 1895 Röntgen discovered that a high voltage dis charge between electrodes in a gas at very low pressureproduces a penetrating radiation which causes certainmaterials to fluoresce visible light [6]. He observed thatif the voltage is sufficiently high, the radiation, whichhe called X rays, can penetrate a hand, casting shadowsof the bones on a fluorescent screen. Within a monthhis discovery created a world wide sensation. It sooncame to be understood that electrons, emitted from thenegative electrode (cathode) of the discharge tube, andaccelerated by the applied voltage, emit electromagneticradiation (bremsstrahlung X rays) when they collide withthe positive electrode (anode) or the walls of the tube.Röntgen thought, tentatively and incorrectly, that thenew rays were longitudinal electromagnetic waves. Thehigh frequency transverse wave nature of X rays was fi nally proved sixteen years later by von Laue’s discoveryof the diffraction of X rays by crystals. The significanceof Röntgen’s discovery for medical diagnosis was quicklyrecognized. Kaisers, queens and lesser folk shared thewonder of gazing at the interior structure of living bodieswithout cutting them open. In the 1930’s children couldspend hours at the shoe store amusing themselves by wig gling their toes in the X ray fluoroscope used to judge thefit of new shoes. Millions had their chests regularly exam ined by high dose X ray photography for signs of tubercu losis. Since the 1940’s it has been known that irradiationof genetic material in cells by X rays and other ionizingradiations induces changes that can cause cancer. Expo sures significantly exceeding that due to natural sourcessuch as cosmic rays and background radioactivity musttherefore be avoided. The sources used in the present ex periment have been approved by the MIT radiation safetyoffice for educational use. They are not dangerous if han dled with appropriate caution. You are urged to deter mine the exposures you may receive in various manipula tions of the laboratory sources by making suitable mea surements with the laboratory radiation exposure meter.The consequences of Röntgen’s discovery for physics wereprofound. Six years previously Hertz had discovered elec tromagnetic radiation (gigahertz radio waves) with wave lengths a million times longer than that of visible light.Röntgen’s work showed how to generate electromagneticradiation with wavelengths ten thousand times shorter.Such wavelengths are comparable to atomic dimensions.As a consequence, X rays proved to be a powerful meansfor exploring the atomic structure of matter as well as thestructure of atoms themselves. Over the next 30 years thediscovery and measurement of X ray phenomena playeda central role in the development of the modern quan tum theory of matter and radiation. Among the mostimportant landmarks were von Laue’s discovery of X raydiffraction by crystals, Moseley’s discovery of the rela tion between atomic number and the wavelengths of thecharacteristic X rays emitted by the elements, Siegbahn’sstudies in X Ray spectroscopy [7] and Compton’s discov ery of the quantum character of the scattering of X raysfrom free electrons [8–10]. In the present experiment youwill use a germanium solid state X ray spectrometer tostudy a variety of phenomena involving the interactionsId: 31.xrays.tex,v 1.21 2005/02/08 20:41:09 sewell Exp
Id: 31.xrays.tex,v 1.21 2005/02/08 20:41:09 sewell Expof high energy photons and matter. The introductorypart is a study of X ray production by irradiation of mat ter by electrons and X rays. It is intended to familiarizeyou with the equipment and some of the basic physics ofX rays. The rest is a menu of possible studies you canpursue as time permits.The sub discipline of X Ray physics involves a certainamount of nomenclature and notation that you will needto become familiar with BEFORE performing this lab.A term diagram for the X ray levels of a heavy element,showing the transitions giving rise to the K, L, and Mlines can be found in Reference [10] page 630 and also onthe Junior Lab web site. This is necessary useful for read ing some of the original literature on X Rays. In morerecent times, a more intuitive notation has become dom inant (see Reference [3]) and you should become familiarwith converting between both notations.TABLE I: Correspondence between X ray diagram levels andelectron configurations. A more complete table can be foundin [3].LevelKL1L2L3M1M2M3M4M5Electronconfig.1s 12s 12p 12p3/2 13s 13p 13p3/2 13d3/2 13d5/2 1LevelN1N2N3N4N5N6N7Electronconfig.4s 14p 14p3/2 14d3/2 14d5/2 14f5/2 14f7/2 1LevelO1O2O3O4O5O6O7Electronconfig.5s 15p 15p3/2 15d3/2 15d5/2 15f5/2 15f7/2 1TABLE II: Correspondence between the Siegbahn (older) andIUPAC (newer) notations. A more complete table can befound in [3].SiegbahnKα1Kα2Kβ1Kβ2 IIUPACK L3K L2K M3K N3SiegbahnLα1Lα2Lβ1Lβ2IUPACL3 M5L3 M4L2 M4L3 N5Transitions between X ray levels are denoted by thelevel symbols for initial and final states separated by ahypen. The initial state is placed first, irrespective ofthe energetic ordering. Much of the older literature inthis field uses the “Siegbahn” notation to describe X ray transitions and Table II shows the correspondencebetween the two notations. As an example: K L3 (Kα1in the Siegbahn notation) denotes the filling of a 1s holeby a 2p3/2 electron.3.2EXPERIMENTAL ARRANGEMENTThe detector is a solid state ionization chamber madeof a single crystal of very pure germanium. The crystal ismounted behind a thin beryllium window in a vacuum ona copper “cold finger” which dips into liquid nitrogen con tained in a large Dewar. This arrangement conducts heataway from the crystal and keeps the detector at a tem perature of 80 K, which assures that the rate at whichelectrons are thermally excited into the conduction bandof the crystal is very low. The crystal is reverse biasedby 700 VDC in order to sweep out any conductionelectrons that do appear, either as a result of rare ther mal excitations or as a result of excitation by energeticcharged particles such as the photoelectrons ejected fromthe germanium atoms by incident X rays.CAUTION – The field effect transistor in thepreamplifier attached to the Ge detector is easilydamaged and costly to replace. Please observethe following precautions:1. Be sure the preamplifier is powered (from the backof the NIM bin) before turning on the high voltagebias.2. SLOWLY raise the bias voltage to 700 VDC (besure of the polarity!).3. Ask an instructor to oversee your first use of thesystem.An X ray photon can interact with the germaniumcrystal by:1. Photoelectric absorption by an atom, resulting inthe disappearance of the photon and the creationof an excited ion through ejection from the atom ofan electron with an amount of kinetic energy equalto the original energy of the photon less the energy(binding energy) required to remove the electronfrom the atom.2. Compton scattering by a loosely bound electron,resulting in a recoil electron and a scattered photon;3. Pair creation, if the energy of the incident photonis sufficient (hν 2me c2 ). The result is the disap pearance of the photon and the materialization ofan electron and positron with an amount of energyapproximately equal to that of the incident photonless the rest energy of two electrons.4. Coherent scattering by the bound electrons of anatom, resulting in a scattered photon of slightly re duced energy and changed direction, and negligibleexcitation of the crystal.Interaction of an incident photon by process 1,2, or3 is the start of a complex degradation process that in volves multiple Coulomb interactions of the Compton recoil, photoelectric ejected, or pair created electrons
Id: 31.xrays.tex,v 1.21 2005/02/08 20:41:09 sewell Exp3FIG. 1: Qualitative term diagram from [11].with atoms of the crystal, as well as interaction or es cape of photons that may emerge from the interactions.The Coulomb interactions excite valence electrons intothe conduction band, thereby giving rise to mobile chargethat is swept by the bias voltage onto the emitter of theFET in the preamplifier. In the case of a primary pho toelectric interaction, the excited ion, missing an inner shell electron, decays by a cascade of transitions in whichelectrons from outer shells fall inward, terminating fi nally with the capture of a stray electron into the va lence shell. Each decay transition produces a photonof a certain characteristic energy which may interact inthe crystal with the production of more recoil or photo electrically ejected electrons. In pair production, if thepositron comes to rest in the crystal it will combine withan electron and annihilate with the production of two511 Kev photons traveling in opposite directions. If allthe energy of the original photon finally appears as thekinetic energy of secondary electrons in the crystal, thenthe amplitude of the resulting charge pulse will be accu rately proportional to the energy of the incident photon;this is the ideal situation desired in X ray spectroscopy.On the other hand, if one or more of the secondary pho tons escapes from the crystal, the resulting charge pulsewill be smaller, resulting in a broadened spectral line or,more importantly, in a separate “escape” peak in thespectrum, corresponding to the escape of precisely oneenergetic photon such as the K X ray photon emitted bya germanium atom that has photoelectrically absorbedthe incident photon. Figure 1 is a block diagram of theelectronic equipment . The detector is connected througha preamplifier to an amplifier, and thence to a Perkin Elmer/Ortec multichannel analyzer (MCA). The pream plifier is permanently mounted on the detector. The am plifier is a spectroscopy grade unit, with coarse gain vari able in steps and a continuous fine gain control. Thesignal pulses from the preamplifier are positive. Positivepulses from the amplifier are fed directly to the ADC in put of the MCA which takes 0 10 volt positive pulseswith widths greater than 2 µs. (Use of the bipolar out put assures that the baseline is restored after each pulse.)The MCA sorts the pulses according to their amplitudesand records the number of pulses in each of 2048 ampli tude intervals. A histogram display of these numbers isgenerated by the MCA and represents the energy spec trum of the detected X rays.Whenever you start up the system or make a change itis wise to check the proper function of the preamplifier,amplifier, and MCA by examining with an oscilloscopethe pulses at the output of amplifier, and to check theoverall performance of the system with the aid of thepulser. In particular, you should check that the shapeand polarity of the pulses into each unit are correct, andthat the amplitudes of the pulses you wish to analyze arein the proper range as they enter the MCA. The outputcurrent from the detector is accumulated on a small ca
Id: 31.xrays.tex,v 1.21 2005/02/08 20:41:09 sewell Expthe original papers in References [12, 13]).PulserTEDetectorPre-amplifierAmplifierMCA (in PC)-700 VDC BiasDetectorBias SupplyFIG. 2: Schematic diagram of the circuit arrangement forX ray spectroscopy.pacitor connected to the emitter of the input FET in thepreamplifier. The capacitor is discharged automaticallyby an auxiliary circuit whenever the accumulated chargeexceeds a certain limit. Each discharge produces a pulseof fixed height that appears in one or two channels ofthe MCA at the high energy end of the spectrum. Therate of these discharges varies according to the intensityof the radiation being measured. Care must be taken notto mistake the resulting spectrum feature for a line in theX ray spectrum being recorded.3.1.STARTING UPTurn on the NIM bin power supply, the PC, and theoscilloscope. Run the MCA control software called Genie2000 from the Windows desktop (details of the MCAsoftware are contained in the appendix). Connect theamplifier output to the MCA and the oscilloscope. Turnon the high voltage supply and gradually apply the biasvoltage of 700 volts while monitoring the detectoroutput on the oscilloscope.Be sure you apply a negative bias voltage; apositive high voltage bias may damage the detec tor.Place the 55 F e source a few inches in front of the Ge1detector window. (The window is made of beryllium 1000inch thick!. A guard has been placed over it to preventaccidental touching and breaking of the fragile foil, whichmust be as thin as possible to allow low energy X rays tobe detected and yet strong enough to hold the vacuum.)Adjust the gain of the amplifier so that at its output theprominent 5.89 keV K L line of 55 M n appears on theoscilloscope as a concentration of pulses with amplitudesnear 1 volt . The amplifier should work with a coarsegain of about 300. Vary the distance between source anddetector and note if the amplitude of the line begins tosag due to too high a counting rate. Back off sufficientlyto insure a stable response. Accumulate a spectrum withthe MCA, and adjust the gains so that the Mn K Lline is centered on the left side of the display.4.4OBSERVATIONS1. The E versus Z relations (Moseley’s law) for thevarious series of characteristic K and L X rays (See2. The fine structure splittings of the K and L shellenergy levels.3. Ratios of the maximum electron recoil energy tothe incident photon energy for Compton scatteringof photons.4. Attenuation cross sections of carbon, aluminumand lead for X rays of several different energies.5. The jump in absorption cross section at a K edge.Keep notes of the settings used in all your measure ments so you can return to them quickly if desired.Analyze the spectra as you take them by using the cur sor to determine peak position and the full width at halfmaximum (FWHM), and the region of interest (ROI) fea ture to determine total counts and area under the peaks.Do not leave simple analysis of data for later. In partic ular, where graphical display of the data is appropriate,have graph paper at hand and make a plot as you goalong so that you can see what is happening. Record allpertinent information about each file in your notebook.4.1.PRODUCTION OF ENERGETIC PHOTONSThe purpose of the following experiments is to famil iarize you with the various processes in which energeticphotons in the energy range above several keV can beproduced. The name “X ray” is generally given to sucha photon if it is emitted by a free or bound electron andhas an energy in the range from 0.1 to 100 keV. Below0.1 keV lies the “extreme ultraviolet”; above is the regionof “gamma rays”. Photons emitted directly by nuclei aregenerally called gamma rays even if their energy is inthe conventional X ray range. The high energy photonproduction processes you will explore are:1. Bremsstrahlung (“Braking radiation”): An ener getic electron which undergoes a sudden accelera tion caused by interaction with a high Z nucleus hasa high probability of emitting a “bremsstrahlung”photon with an energy in the range from 0 to thefull kinetic energy of the electron. This is the pro cess that occurred in Röntgen’s discovery experi ment when electrons accelerated in the dischargestruck the glass wall of the tube.2. X ray fluorescence induced by energeticcharged particles: When an energetic electronor other charged particle (e.g.an alpha particle) in teracts with an atom it may eject an electron fromone of the inner shells. The resulting ion relaxesfrom its excited state by a cascade of transitions inwhich electrons from outer shells fall inward untilno vacancy remains. Each transition gives rise toa photon with a characteristic energy. A photon
Id: 31.xrays.tex,v 1.21 2005/02/08 20:41:09 sewell Expproduced when an outer electron falls into a holein the n 1,2, and 3 shells are called K, L, and MX rays, respectively.3. X ray fluorescence induced by X rays: A pho ton with sufficient energy may interact with anatom to eject an electron from an inner shell inwhat is called a “photoelectric” absorption process.The subsequent relaxation of the excited ion pro duces the same characteristic X rays as in electronbombardment.4. Emission of photons by the decay of excitednuclei: One example of this process is the decayof the excited nucleus of 57 F e created by the betadecay (K electron capture) of 57 Co as describedin Melissinos (2003). Under certain circumstancesthis decay yields photons with energies in an ex tremely narrow range near 14.4 keV which can beexploited in ”Mössbauer” spectroscopy. In addi tion, decay of the excited 57 F e electronic structurewhich results from the capture of the K electrongives rise to the characteristic X ray photons ofiron.5. Annihilation of electron positron pairs: Someunstable nuclei (e.g. 22 N a) undergo a beta decayprocess in which a proton in the nucleus is trans formed into a neutron with the emission of apositron (anti electron) and an electron neutrinoaccording to the schemep n e νe(1)The ejected positron eventually interacts with anelectron in the surrounding material and annihi lates with the production of photons. Such anni hilations usually yield two photons which, in thecenter of mass, travel in exactly opposite directionsand each with an energy of precisely me c2 in ac cordance with the conservation of momentum andenergy.5.5the target consists of a bremsstrahlung continuum withan energy cutoff at hcλ V e (V is the voltage of thepower supply), and narrow lines with wavelengths char acteristic of the target material. In this experiment thesource of energetic electrons is several millicuries of 90 Srwhich decays according to the schemeSr38 90 Y39 e νeY39 90 Zr40 e νe9090The source is contained in an aluminum and lead linedcontainer (see Figure 2) which can be placed on the smallwooden stand next to the detector so that the hole be hind the lead shutter is aligned with the entrance windowof the detector. CAUTION: Avoid exposing yourhands to the radiation emerging from the hole inthe lead lined box. The 90 Sr source is quite strong(several millicuries) and the electrons which itemits readily bounce off lead nuclei in all direc tions, including out through the hole.Observe the spectrum of pulses with nothing in the45 slot. Then put a thin (1/4“ thick) slab of lead inthe 45 slot so that the bet
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